Statistically recognize faces based on hidden markov models
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Statistically Recognize Faces Based on Hidden Markov Models. Presented by Timothy Hsiao-Yi Chin Rahul Mody. What is Hidden Markov Model?. Its underlying is a Markov Chain.

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Statistically Recognize Faces Based on Hidden Markov Models

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Statistically recognize faces based on hidden markov models

Statistically Recognize Faces Based on Hidden Markov Models

Presented by

Timothy Hsiao-Yi Chin

Rahul Mody

E6886 Project


What is hidden markov model

What is Hidden Markov Model?

Its underlying is a Markov Chain.

An HMM, at each unit of time, a single observation is generated from the current state according to the probability distribution, which is dependent on this state.

E6886 Project


Mathematical notation of hmm

Mathematical Notation of HMM

  • Suppose that there are T states {S1, …, ST} and the probability between state i and j is Pij. Observation of system can be defined as ot at time t. Let bSi(oi) be the probability function of ot at time t. Lastly, we have the initial probability , i = 1, …, n of Markov chain. Then the likelihood of the observing the sequence o is

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Which probability function of o t

Which probability function of ot?

  • In HMM framework, observation o is assumed to be governed by the density of a Gaussian mixture distribution.

  • Where k is the dimension of ot, and where oiand

    are the mean vector and covariance matrix, respectively

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Re estimation of mean covariances and the transition probabilities

Re-estimation of mean, covariances, and the transition probabilities

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Example a markov model

70%

60%

25%

28%

5%

12%

70%

10%

20%

Example: A Markov Model*

Sunny

Rainy

Snowy

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Represent it as a markov model

Represent it as a Markov Model*

  • States:

  • State transition probabilities:

  • Initial state distribution:

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What is sequence o in this example

What is sequence o in this example?*

  • Sequence o:

  • The probability could be computed by the conditional probability:

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Example a hmm

Example: A HMM*

5%

70%

80%

20%

20%

Sunny

60%

Rainy

15%

38%

2%

5%

5%

75%

10%

75%

Snowy

20%

45%

5%

50%

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What other parameters will be needed

What other parameters will be needed?

  • If we can not see what is inside blue circle, what can we actually see?

  • Observations:

  • Observation probabilities:

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Forward backward algorithm forward

Forward-Backward Algorithm: Forward

  • If Observation probability is

  • then

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Forward backward algorithm backward

Forward-Backward Algorithm: Backward

  • If there is a

  • Then

  • The Forward-Backward Algorithm tells us that

  • for any time t

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Face identification using hmm

Face identification using HMM

  • An Observation sequence is extracted from the unknown face, the likelihood of each HMM generating this face could be computed.

  • In theory, the likelihood is

  • The maximum P(O) can identifies the unknown faces.

  • However, it takes too much time to compute.

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Face identification using hmm1

Face identification using HMM

  • In practice, we only need one S sequence

    which maximizes

  • This is a dynamic programming optimization procedure.

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Viterbi algorithm

Viterbi Algorithm

  • Given a S sequence, a dynamic programming approach to solve this problem

  • where

  • By induction, the max Probability in state i+1 at time t+1 is based on the max probability in state I at time t.

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Algorithm itself

Algorithm itself

  • Initialization

    where denotes the collection of that sequence which is based on max

  • Recursion:

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Algorithm itself 2

Algorithm itself (2)

  • Termination

  • Sequence constructing from T to t

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So far we have this block diagram

So far we have this block diagram

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Face detection

Face Detection

  • In simple face recognition framework, the picture is assumed to be a frontal view of a single person and the background is monochrome.

  • This project assumes that with the techniques of face detection, the performance of face recognition may be better than the approach presented above.

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Acknowledgement

Acknowledgement

  • The authors of this presentation slides would like to give thanks to Dr. Doan, UIUC.

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Reference

Reference

  • [1] Ferdinando Samaria, and Steve Young, HMM-based architecture for face identification.

  • [2] Jia, Li, Amir Najmi, and Robert M. Gray, Image Classification by a Two-Dimensional Hidden Markov Model

  • [3] Ming-Hsuan Yang, David J. Kriegman, Narendra Ahuja, Detecting Faces In Images: A survey

  • [4] T.K. Leung, M. C. Burl, and P. Perona, Finding Faces in Cluttered Scenes using Random Labeled Graph Matching

  • [5] James Wayman, Anil Jain, Davide Maltoni, and Dario Maio, Biometric Systems, Springer, 2005

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